ME3402, VB6'0

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ME3402, VB6.0

• Dr. C.M. Hsiung
• June 10, 2005
• Lesson 15

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Lesson 15

• Ordinary Differential Equation
• Eulers Method

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Contents

• Quiz (15 min)
• Review Numerical Integration (10 min)
• ODE (30 min)
• Homework (5 min)
• On-line practice (2 hrs)

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Quiz

• Base on the Simpsons rule to
• Find and print out Integral(f(x),b,a) where
• f(x) x2 a0, b1
• The error should be less than 1/100

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Rev Numerical Integration

• Simpsons rule
• integral(f(x),x2,x0)
• h f(x0)4f(x1)f(x2)/6
• where
• hx2-x0
• x1(x0x2)/2

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Ordinary Differential Equation

• Many mechanical engineering problems are in form
  of ODE, such as equations in
• Kinematics, Dynamics, Control.
• You will learn the Analytical Solution of ODE in
  Engineering Math next semester
• Here, Ill just give you a taste of it. So, enjoy
  yourself

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An ordinary differential equation

• dy/dt f(t, y), alttltb, y(a)p0
• find y(t)
• example
• y 1tsin(ty) 0lttlt2, y(0)0
• find y(t)

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Eulers Method

• To approximate the solution of
• yf(t,y), alttltb, y(a)ya
• at (N1) equally spaced numbers in a, b
• Input a, b, N, ya
• Output approximation w to y at the (N1) values
  of t

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Eulers Method

• Step 1 Set h(b-a)/N
• ta wya Output (t, w)
• Step 2 For i1,2,N do Step 3,4
• Step 3 Set wwh f(t,w)
• t a i h
• Step 4 Output (t,w)
• Step 5 Stop

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Online Practice

• Understand and Use the Eulers Method tosolve
• y -yt1, 0lttlt1, y(0)1
• suppose N10
• You gain 10 bonus points to by finishing the
  practice in class

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Homework

• Understand and Use the Eulers Method tosolve
• y t2, 0lttlt2, y(0)0
• control your error at every point to be less
  than 0.01

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The End

• God helps those who
• Help themselves